This paper presents a novel high-power rotary waveguide phase shifter based on circular polarizers specifically engineered for high-power microwave (HPM) applications. The phase shifter is capable of performing a precise 360° linear phase shift through rotation and consists of three parts: a linear polarized to left-handed circular polarized (LP-LHCP) mode converter, a left-handed to right-handed circular polarized (LH-RHCP) mode converter, and a linear polarized to right-handed circular polarized (LP-RHCP) mode converter. The paper analyzes the phase shifting principle, optimizes the three parts of the X-band rotary waveguide phase shifter, and conducts simulation studies on the entire phase shifter made of aluminum. The results show that the reflection is less than -20dB and the transmission efficiency is over 95% within 9.5GHz to 10.2GHz. The phase shift has a linear relationship with the rotation angle by a factor of two within this frequency range. Specifically, the phase shifter can achieve a linear phase shift of 360° when rotated from 0° to 180°, with a maximum deviation of less than 1.2°. Moreover, the power-handling capacity of the phase shifter in vacuum exceeds 242mW.